Solve the following differential equations using Taylor series
centered at 0. It’s enough to find the recurrence relation and the
first 3 terms of the series.
(a) y''− 2y' + y = 0
(b) y'' + xy' + 2y = 0
(c) (2 + x^2 )y'' − xy'+ 4y = 0
x2 y" + (x2+x) y’
+(2x-1) y = 0,
Find the general solution of y1 with
r1 and calculate the coefficient up to
c4 and also find the general expression of the
recursion formula, (recursion formula for
y1)
Find the general solution of y2 based on
theorem 4.3.1. (Hint, set d2 = 0)